Question

Jika (x+5), (x+1), dan (x-1) adalah tiga suku pertama deret geometri tak hingga, maka jumlah semua suku-sukunya adalah...

Answer 1

(x + 1)² = (x + 5)(x - 1)
x² + 2x + 1 = x² + 4x - 5
2x + 1 = 4x - 5
2x = 6
x = 3

barisannya:
8, 4, 2, ...

S~ = a/(1 - r)
     = 8/(1 - 1/2)
     = 8/(1/2)
     = 16

Answer 2

U1 = a = x+5
u2 = x+1
u3 = x-1
rasio:
u2/u1 = u3/u2
(x+1)/(x+5) = (x-1)/(x+1)
(x+1)(x+1) = (x+5)(x-1)
x²+2x+1 = x²+4x-5
x²+2x-x²-4x = -5-1
-2x = -6
x = 3
a = x+5
   = 3+5
   = 8
r = (x+1)/(x+5)
  = (3+1)/(3+5)
  = 4/8
  = 1/2

sn = a/(1-r)
     = 8/(1-1/2)
     = 8/(1/2)
     = 16